Medical devices, for example, stents, prosthetic valves, and other implantable medical devices, can be compressed to facilitate delivery of the devices at an implantation site in a subject's body, for example, a native cardiac valve. The medical devices are delivered to the implantation site via a delivery device (for example, a catheter) having radial dimensions that are smaller than the unconstrained or expanded radial dimensions of the medical device (i.e., the radial dimensions of the medical device, when the medical device is in an unconstrained state), and/or that are smaller than the dimensions of the medical device upon deployment of the medical device at the implantation site, a native cardiac valve. To facilitate insertion of such a medical device into or on the delivery device, the medical device is compressed (typically, at least radially).